MATHEMATICAL PROGRAMMING ALGORITHMS FOR NETWORK OPTIMIZATION PROBLEMS

In the thesis we consider combinatorial optimization problems that are defined by means of networks. These problems arise when we need to take effective decisions to build or manage network structures, both satisfying the design constraints and minimizing the costs. In the thesis we focus our attention on the four following problems: - The Multicast Routing and Wavelength Assignment with Delay Constraint in WDM networks with heterogeneous capabilities (MRWADC) problem: this problem arises in the telecommunications industry and it requires to define an efficient way to make multicast transmissions on a WDM optical network. In more formal terms, to solve the MRWADC problem we need to identify, in a given directed graph that models the WDM optical network, a set of arborescences that connect the source of the transmission to all its destinations. These arborescences need to satisfy several quality-of-service constraints and need to take into account the heterogeneity of the electronic devices belonging to the WDM network. - The Homogeneous Area Problem (HAP): this problem arises from a particular requirement of an intermediate level of the Italian government called province. Each province needs to coordinate the common activities of the towns that belong to its territory. To practically perform its coordination role, the province of Milan created a customer care layer composed by a certain number of employees that have the task to support the towns of the province in their administrative works. For the sake of efficiency, the employees of this customer care layer have been partitioned in small groups and each group is assigned to a particular subset of towns that have in common a large number of activities. The HAP requires to identify the set of towns assigned to each group in order to minimize the redundancies generated by the towns that, despite having some activities in common, have been assigned to different groups. Since, for both historical and practical reasons, the towns in a particular subset need to be adjacent, the HAP can be effectively modeled as a particular graph partitioning problem that requires the connectivity of the obtained subgraphs and the satisfaction of nonlinear knapsack constraints. - Knapsack Prize Collecting Steiner Tree Problem (KPCSTP): to implement a Column Generation algorithm for the MRWADC problem and for the HAP, we need also to solve the two corresponding pricing problems. These two problems are very similar, both of them require to find an arborescence, contained in a given directed weighted graph, that minimizes the difference between its cost and the prizes associated with the spanned nodes. The two problems differ in the side constraints that their feasible solutions need to satisfy and in the way in which the cost of an arborescence is defined. The ILP formulations and the resolution methods that we developed to tackle these two problems have many characteristics in common with the ones used to solve other similar problems. To exemplify these similarities and to summarize and extend the techniques that we developed for the MRWADC problem and for the HAP, we also considered the KPCSTP. This problem requires to find a tree that minimizes the difference between the cost of the used arcs and the profits of the spanned nodes. However, not all trees are feasible: the sum of the weights of the nodes spanned by a feasible tree cannot exceed a given weight threshold. In the thesis we propose a computational comparison among several optimization methods for the KPCSTP that have been either already proposed in the literature or obtained modifying our ILP formulations for the two previous pricing problems. - The Train Design Optimization (TDO) problem: this problem was the topic of the second problem solving competition, sponsored in 2011 by the Railway Application Section (RAS) of the Institute for Operations Research and the Management Sciences (INFORMS). We participated to the contest and we won the second prize. After the competition, we continued to work on the TDO problem and in the thesis we describe the improved method that we have obtained at the end of this work. The TDO problem arises in the freight railroad industry. Typically, a freight railroad company receives requests from customers to transport a set of railcars from an origin rail yard to a destination rail yard. To satisfy these requests, the company first aggregates the railcars having the same origin and the same destination in larger blocks, and then it defines a trip plan to transport the obtained blocks to their correct destinations. The TDO problem requires to identify a trip plan that efficiently uses the limited resources of the considered rail company. More formally, given a railway network, a set of blocks and the segments of the network in which a crew can legally drive a train, the TDO problem requires to define a set of trains and the way in which the given blocks can be transported to their destinations by these trains, both satisfying operational constraints and minimizing the transportation costs

Loss-free architectures in optical burst switched networks for a reliable and dynamic optical layer

For the last three decades, the optical fiber has been a quite systematic response to dimensioning issues in the Internet. Originally restricted to long haul networks, the optical network has gradually descended the network hierarchy to discard the bottlenecks. In the 90's, metropolitan networks became optical. Today, optical fibers are deployed in access networks and reach the users. In a near future, besides wireless access and local area networks, all networks in the network hierarchy may be made of fibers, in order to support current services (HDTV) and the emergence of new applications (3D-TV newly commercialized in USA). The deployment of such greedy applications will initiate an upward upgrade. The first step may be the Metropolitan Area Networks (MANs), not only because of the traffic growth, but also because of the variety of served applications, each with a specific traffic profile. The current optical layer is of mitigated efficiency, dealing with unforeseen events. The lack of reactivity is mainly due to the slow switching devices: any on-line decision of the optical layer is delayed by the configuration of the. devices. When the optical network has been extended in the MANs, a lot of efforts has been deployed to improve the reactivity of the optical layer. The Optical Circuit Switching paradigm (OCS) has been improved but it ultimately relies on off-line configuration of the optical devices. Optical Burst Switching (OBS) can be viewed as a highly flexible evolution of OCS, that operates five order of magnitude faster. Within this 'architecture, the loss-free guaranty can be abandoned in order to improve the reactivity of the optical layer. Indeed, reliability and reactivity appear as antagonists properties and getting closer to either of them mitigates the other. This thesis aims at proposing a solution to achieve reliable transmission over a dynamic optical layer. Focusing on OBS networks, our objective is to solve the contention issue without mitigating the reactivity. After the consideration of contention avoidance mechanisms with routing constraints similar as in OCS networks, we investigate the reactive solutions that intend to solve the contentions. None of the available contention resolution scheme can ensure the 100% efficiency that leads to loss-free transmission. An attractive solution is the recourse to electrical buffering, but it is notoriously disregarded because (1) it may highly impact the delays and (2) loss can occur due to buffer overflows. The efficiency of translucent architectures thus highly depends on the buffer availability, that can be improved by reducing the time spent in the buffers and the contention rate. We show that traffic grooming can highly reduce the emission delay, and consequently the buffer occupancy. In a first architecture, traffic grooming is enabled by a translucent core node architecture, capable to re-aggregate incoming bursts. The re-aggregation is mandatory to "de-groom" the bursts in the core network (i.e., to demultiplex the content of a burst). On the one hand, the re-aggregation highly reduces the loss probability, but on the other hand, it absorbs the benefits of traffic grooming. Finally, dynamic access to re-aggregation for contention resolution, despite the significant reduction of the contention rate, dramatically impacts the end-to-end delay and the memory requirement. We thus propose a second architecture, called CAROBS, that exploits traffic grooming in the optical domain. This framework is fully dynamic and can be used jointly with our translucent architecture that performs re-aggregation. As the (de)grooming operations do not involve re-aggregation, the translucent module can be restricted to contention resolution. As a result, the volume of data submitted to re-aggregation is drastically reduced and loss-free transmission can be reached with the same reactivity, end-to-end delay and memory requirement as a native OBS networ

p-Cycle Based Protection in WDM Mesh Networks

Abstract p-Cycle Based Protection in WDM Mesh Networks Honghui Li, Ph.D. Concordia University, 2012 WDM techniques enable single fiber to carry huge amount of data. However, optical WDM networks are prone to failures, and therefore survivability is a very important requirement in the design of optical networks. In the context of network survivability, p-cycle based schemes attracted extensive research interests as they well balance the recovery speed and the capacity efficiency. Towards the design of p-cycle based survivableWDM mesh networks, some issues still need to be addressed. The conventional p-cycle design models and solution methods suffers from scalability issues. Besides, most studies on the design of p-cycle based schemes only cope with single link failures without any concern about single node failures. Moreover, loop backs may exist in the recovery paths along p-cycles, which lead to unnecessary stretching of the recovery path lengths. This thesis investigates the scalable and efficient design of segment p-cycles against single link failures. The optimization models and their solutions rely on large-scale optimization techniques, namely, Column Generation (CG) modeling and solution, where segment pcycle candidates are dynamically generated during the optimization process. To ensure full node protection in the context of link p-cycles, we propose an efficient protection scheme, called node p-cycles, and develop a scalable optimization design model. It is shown that, depending on the network topology, node p-cycles sometimes outperform path p-cycles in iii terms of capacity efficiency. Also, an enhanced segment p-cycle scheme is proposed, entitled segment Np-cycles, for full link and node protection. Again, the CG-based optimization models are developed for the design of segment Np-cycles. Two objectives are considered, minimizing the spare capacity usage and minimizing the CAPEX cost. It is shown that segment Np-cycles can ensure full node protection with marginal extra cost in comparison with segment p-cycles for link protection. Segment Np-cycles provide faster recovery speed than path p-cycles although they are slightly more costly than path p-cycles. Furthermore, we propose the shortcut p-cycle scheme, i.e., p-cycles free of loop backs for full node and link protection, in addition to shortcuts in the protection paths. A CG-based optimization model for the design of shortcut p-cycles is formulated as well. It is shown that, for full node protection, shortcut p-cycles have advantages over path p-cycles with respect to capacity efficiency and recovery speed. We have studied a whole sequence of protection schemes from link p-cycles to path p-cycles, and concluded that the best compromise is the segment Np-cycle scheme for full node protection with respect to capacity efficiency and recovery time. Therefore, this thesis offers to network operators several interesting alternatives to path p-cycles in the design of survivable WDM mesh networks against any single link/node failures